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Search: id:A156636
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| 1820, 6214, 10608, 15002, 19396, 23790, 28184, 32578, 36972, 41366, 45760, 50154, 54548, 58942, 63336, 67730, 72124, 76518, 80912, 85306, 89700, 94094, 98488, 102882, 107276, 111670, 116064, 120458, 124852, 129246, 133640, 138034, 142428
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OFFSET
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1,1
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COMMENT
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Arises in solving Pell equations of the form X^2 - A*Y^2 = 1.
Let n=[A156718] (70,99,239,268,408,437,...,). If A=[A156640] (29,338,985,...,) or A=[156639] (29,58,425) =(n^2+1)/13^2 , Y=26*n, [A156636] (1820,6214,10608,...,) or Y=[A156627] (2574,6968,11362,...,) and X=2*n^2+1 [A156721] (9801,19603,143649,...,) or X=[A156735] (9801,114243,332929,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=70, A=29, Y=1820, X=9801; 9801^2-29*1820^2=1; n=99, A=58, Y=2574, X=19603; 19603^2-58*2574^2=1; n=239, A=338, Y=6214, X=114243; 114243^2-338*6214^2=1; n=268, A=425, Y=6968, X=143649; 143649^2-425*6968^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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EXAMPLE
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For n=0, a(0)=1820; n=1, a(1)=6214; n=2, a(2)=10608
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CROSSREFS
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Cf. A156627
Cf. A156640, A156639, A156718, A156721, A156735 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A122477 A134155 A058954 this_sequence A124073 A167266 A151644
Adjacent sequences: A156633 A156634 A156635 this_sequence A156637 A156638 A156639
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 15 2009
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